Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
Multiple sclerosis (MS) is a chronic, inflammatory demyelinating disease of central nervous system with complex etiopathogenesis that impacts young adults (Lee et al., 2015), and MS impacts younger and middle aged character and leads to a range of disabilities that can alter their daily routines (Yara et al, 2010). Although, the exact cause of MS is still undetermined, the disease is mediated by adaptive immunity through the infiltration of T cells into the central nervous system (Bjelobaba et al, 2017). MS causes the Focal neurological symptomsand biochemical changes in the molecular level and the variation of neural cells such as loss or alteration of sensation, motor function, visible signs such as blurred vision or transient blindness,
... Show MoreThe aim of this work was to develop and validate a rapid and low cost method for estimation of ibuprofen in pharmaceutical suspensions using Reverse-Phase High Performance Liquid Chromatography. The proposed method was conducted and validated according to International Conference on Harmonization (ICH) requirements. The chromatographic parameters were as follows: column of octyldecylsilyl C18 with dimensions (150 × 4.6) mm, mobile phase composed of acetonitrile with phosphoric acid with a ratio of 50 to 50 each using isocratic mode, flow rate of 1.5 mL/min and injection volume of 5 μL. The detection was carried out using UV detector at 220 nm. The method was validated and showed short retention time for ibuprofen peak at 7.651 min, wit
... Show MoreA square experimental arena with vegetation on one interior side was deployed in a Sharjah, United Arab Emirates desert. Individual darkling beetles (Coleoptera, Tenebrionidae) Akis subtricostata Redtenbacher, 1850 and Trachyderma philistina Reiche and Saulcy, 1857 were placed inside the arena at temperatures ranging between 27 - 49°C. Whether they chose the vegetated side of the arena or not was recorded, as well as how long it took for them to reach the vegetated side, if they chose it. Both species preferred the vegetated side at all temperatures, and the chance of them choosing the vegetated side increased significantly with increasing temperature (logistic regression, p = 0.0096 and p = 0.0003 for
... Show MoreThe aim of this study was Identifying the relation of coordination and kinesthetic perception with artistic performance level in gymnastics skills for students in second class from the college of physical education/ university of Baghdad/ Al - jadreia .The searchers have been used the descriptive method in scanning style .The subject of this search has been taken (45) female - student in second class from the college of physical education/ university of Baghdad . The searchers have reached into specific conclusions concerning with statistic analysis about immoral joint relation between sensitive- kinetic coincidence and realization and with Artistic Performance Level in Gymnastics Skills for Women for second class .The an important recommen
... Show MoreA field experiment was conducted to grow the wheat crop during the fall season 2020 in Karbala province, north of Ain Al-Tamr District in two locations of different textures and parent materials. The first site (calcareous soil) with a sandy loam texture, is located at (44° 40′ 37′) east longitude and (32° 41′ 34′) north latitude, at an altitude of 32 m above sea level, and an area of 20 hectares. As for the second location (gypsum soil) with a loam texture, it is located at a longitude (45° 41′ 39′) east and a latitude (33° 43′ 34′ north) and at an altitude of 33 m above sea level and an area of 20 hectares. To find out the effect of different tillage systems on water productivity and wheat yield under center pivot irri
... Show MoreAutoría: Nuha Mohsin Dhahi. Localización: Revista iberoamericana de psicología del ejercicio y el deporte. Nº. 5, 2022. Artículo de Revista en Dialnet.
Respiratory tract infections in sheep are among the important health problems that affect all sheep ages around the world. Nine bacterial isolates obtained from sheep with respiratory tract infections were selected to be used in the current study. The isolates included 3 Staphylococcus aureus, 4 Klebsiella pneumoniae, and 2 Pseudomonas aeruginosa. Following the primers design by the Primer3Plus software tool and optimization of the conventional polymerase chain reaction (PCR), the primers were validated for their use in the multiplex PCR experiments. The MFEprimer program was used to check the suitability of the primer set combinations for multiplex PCR. The MFEprimer software was successful in designing the multiplex-PCR experiments and de
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